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Those who advocate for monetary incentives in a work environment claim that this type of incentive has the greatest appeal because it allows the winners to do what they want with their winnings. Those in favor of tangible incentives argue that money lacks the emotional appeal of, say, a weekend for two at a romantic country inn or elegant hotel or a weeklong trip to Europe. A few years ago a national tire company, in an effort to improve sales of a new line of tires, decided to test which method鈥攐ffering cash incentives or offering non-cash prizes such as vacations鈥攚as more successful in increasing

sales. The company had $60$ retail sales districts of various sizes across the country and data on the previous sales volume for each district.

(a) Describe a completely randomized design using the $60$ retail sales districts that would help answer this question.

(b) Explain how you would use the table of random digits below to do the randomization that your design requires. Then use your method to assign treatments to the first $3$ experimental units. Show your work clearly.

$$\begin{gathered} 0751188915412671685384569793673233703316 \\ 8148669487605130929700412712382764939950 \end{gathered}$$

(c) One of the company鈥檚 officers suggested that it would be better to use a matched pairs design instead of a completely randomized design. Explain how you would change your design to accomplish this.

Step by step solution

01

Part (a) Step 1: Given information

The numbers are: $$\begin{gathered} 0751188915412671685384569793673233703316 \\ 8148669487605130929700412712382764939950 \end{gathered}$$

02

Part (a) Step 2: Concept

A simple random sample (SRS) of size $n$ is made up of $n$ people chosen from the population with an equal chance of being the sample that is actually chosen.

03

Part (a) Step 3: Explanation

Assign the numbers $01$to $60$to the $60$districts presented. Now, select roughly $30$digits from a random digit number table and assign the monetary incentives to $30$districts. Observe the change in sales of each of the selected $30$ groups over time and conduct a comparison of the $30$ groups.

04

Part (b) Step 1: Explanation

Choose the first two digits and choose the districts if the numbers are between $01$and $60$; otherwise, ignore the districts and repeat the process.

Repeat the process until three retail state districts have been selected.

$2-$digit number Selected retail sales district

$07$ Select retail sales district $07$

$51$ Select retail sales district $51$

$18$ Select retail sales district $18$

The states with the digits $07,51,$and $18$have been selected.

05

Part (c) Step 1: Explanation

Choose the two states with the highest sales, as well as the other districts with the highest sales. Flip a coin to choose the district. Assign the incentive to the state if the head comes up. Continue this approach and compare the results inside each pair to see how things have changed.

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